In this paper we have also provided \(\mathcal {N}=1\)  AdS\(_3\)  superspace extensions to the non-supersymmetric results described above. Specifically, the remarkably simple expression (REF ) for the higher-spin super-Cotton tensor \(\mathfrak {W}_{\alpha (n)}(H)\)  was derived. In the transverse gauge, it was shown that \(\mathfrak {W}_{\alpha (n)}(H)\)  factorises into first-order wave operators (REF ) associated with the so-called type A and type B partially massless superfields. Similar remarks regarding the factorisation of the superconformal higher-spin gauge models (REF ) in an AdS\(_3\)  superspace background follow. The fact that there are two types of partially massless supermultiplets, possessing gauge symmetries (REF ) and (), is a novel feature of three dimensions, and did not occur in four dimensions [1]}.
